数学理论中有关代数簇的研究与工程实践中含参多项式系统都可以视为正维多项式系统。以往处理正维多项式系统的方法都是将其转化为更简单的多项式系统或其他系统。 我们曾经提出过正维多项式系统解的坐标分量的有理单变量表示（RUR）方法，但是由于计算量过大而不实用。本项目将结合这种RUR理论与有理插值逼近，给出一种计算正维多项式系统有理单变量表示的实用算法，将解以坐标分量形式表达出来。这种解的表达方式对于正维代数簇理论的某些研究与含参多项式系统求解使用更为方便。同时我们的方法也为解决输入输出数据均为有理函数的符号计算数据膨胀问题提供一种思路。

Both algebraic varieties in theoretical mathematics and parametric polynomial systems in practice can be considered as positive dimensional polynomial systems, which are usually transferred to simpler polynomial or other systems in previous literature. We have proposed a rational univariate representation (RUR) method for coordinate components of the solutions of positive dimensional polynomial systems before, but it is too heavy for application. In this project we will combine RUR theory and rational interpolation approximation to give a practical algorithm for rational univariate representation of positive dimensional polynomial systems, in which the solutions are represented as coordinate components whose forms are more convenient for investigating positive dimensional algebraic varieties as well as parametric polynomial systems. Also, our method will convey an idea for obviating expression swell in symbolic computation when input and output data are all rational functions.